JPH04323502A - Interferometer - Google Patents

Abstract

PURPOSE:To reduce the change in the difference of light passage lengths generated due to temperature variation by satisfying a specified expression for the physical length of a light passage length correction block. CONSTITUTION:A physical length 1i of a light passage length correction block is set so that an expression 1 is satisfied for di, where ni is refractive index, di is the change in the physical lengths between two beam luminous fluxes for each medium, alphai is rate of change in unit length due to expansion and contraction of the medium except for air, and T is temperature. An interferometer has, for example, a prism P1 which is the light passage length correction block, a prism P2 which is a reflection mirror for bending the light passage, and a polarizing beam splitter 2 which is a beam splitter. Difference in the prism lengths in the proceeding direction of the divided two luminous fluxes is L1, and a distance between the two luminous fluxes is L2. The material of glass is BK7, the wavelength is 632.8nm, and the temperature is 25 deg.C. alpha=7.1X10<-6>/K, n=1.515 (n=n2/n1, where n1 is refractive index of air, and n2 is refractive index of glass). L1=2.1XL2, and when L2=20mm, for example, L1=42mm.

Description

[Detailed description of the invention]

0001

[Industrial Application Field] This invention relates to the reduction of temperature variations in the optical path length of an interferometer.

0002

2. Description of the Related Art FIG. 7 shows the relationship between a laser interferometer and a moving stage to be measured when measuring the coordinates of a moving stage using a conventional two-beam interferometer, such as a laser interferometer.

[0003] This interferometer includes a light source 1 and prisms P3 and P.
4, a polarizing beam splitter 2, a λ/4 plate 3, a movable mirror 4, and a fixed mirror 5.

Laser beam B emitted from laser light source 1
1 is split into two polarization components by a polarization beam splitter 2. The polarized beam B21 having one polarized component that has passed through the polarized beam splitter 2 is passed through the prism P3.
and is reflected by the movable mirror 4. Then, before and after reflection, the polarization plane is rotated by 90 degrees by passing through the λ/4 plate 3 twice, reflected by the polarization beam splitter 2, and incident on the detector 6. A polarized beam B31 having the other polarized component of the laser beam B1 is sent to the polarizing beam splitter 2.
The light is reflected by the prism P4, and then reflected by the fixed mirror 5. And the other polarized beam B
Similarly to 21, the light is incident on the detector 6. Figure 3 shows
8 is an enlarged view of P3 and P4 in FIG. 7. FIG.

[0005]

In the conventional technology, temperature changes cause expansion of the glass and change in the refractive index, resulting in a change in the optical path length difference between the two optical paths on the fixed mirror side and the movable mirror side. As a result, errors occur in the measurements.

An object of the present invention is to provide an interferometer in which such changes in optical path length difference caused by temperature changes are reduced.

[0007]

[Means for Solving the Problems] In order to achieve the object of the present invention, the size of the optical components should be designed so that changes in optical path length due to temperature changes are canceled out in the optical path on the fixed mirror side and the optical path on the movable mirror side. good.

For this purpose, an interferometer divides a beam of light emitted from a light source into a plurality of beams, and each beam passes through one or more media and then interferes with each other. It has a correction block, where the refractive index of each medium is ni (i = 1 to N), the physical length difference between the light beams for each medium is di (i = 1 to N), and each of the above When the change rate per unit length of the physical length difference di due to expansion and contraction of the medium excluding air is αi (i = 1 to N), and the temperature is T, then di is

[0009]

[Math 3]

It is assumed that the physical length li (i=1 to m) of the optical path length correction block described above is set so as to satisfy the following.

[0011]

[Operation] Changes in the optical path length difference due to temperature are caused by changes in the refractive index of the glass, expansion, and changes in the thickness of the air layer due to the expansion of the glass.

The refractive index of each medium is ni (i=1 to N), and the physical length of each ray bundle and each medium is Lij (i=1 to N).
, j=1, 2), the total optical path length for each ray bundle is LH1, LH
If it is 2,

[0013]

[Math 4]

[0014]

When the physical length difference between the light beams for each medium is di (i=1 to N), the temperature is T, and the optical path length difference between the light beams is L, L is given by the following formula.

[0016]

[Math 5]

Therefore, the rate of change of the difference L in optical path length between the beam bundles due to temperature is expressed by the following equation.

[0018]

[Math 6]

Here, the physical length difference di of each medium is
Let αi (i=1 to N) be the rate of change per unit length due to expansion and contraction of a medium other than air, αi is given by the following formula.

[0020]

[Math 7]

[0021] By using equation 7 to transform equation 6 and further setting equation 6=0, the following equation is obtained.

[0022]

[Math. 8]

[0023] Near a certain temperature, ∂ni/∂T, αi,
Since ni is given as a constant, di such as Equation 8
If the combination is made, the optical path length difference will not change depending on the temperature.

[0024]

[Example] When measuring the coordinates of a moving stage using a two-beam interferometer according to the present invention, such as a laser interferometer,
FIG. 1 shows the relationship between the laser interferometer and the moving stage 7 that is the object of measurement.

This interferometer includes a light source 1 which is a laser light source,
A prism P1 which is an optical path length correction block, a prism P2 which is a reflecting mirror for bending the optical path, a polarizing beam splitter 2 which is a beam splitter, a λ/4 plate 3, and a movable mirror 4 which is a second reflecting mirror. and a fixed mirror 5 which is the first reflecting mirror.
and has.

The prism P1, which is an optical path length correction block, the prism P2, which is a reflecting mirror for bending the optical path, and the polarizing beam splitter 2, which is a beam splitter, are integrated into one body.

Laser beam B emitted from laser light source 1
1 is split into two polarization components by a polarization beam splitter 2. The polarized beam B2 having one polarized light component (P polarized light component) that has passed through the polarized beam splitter 2 is
The light passes through the prism P1 and is reflected by the movable mirror 4. Then, before and after reflection, the polarization plane is rotated by 90 degrees by passing through the λ/4 plate 3 twice, becoming an S-polarized light component, reflected by the polarization beam splitter 2, and incident on the detector 6. On the other hand, a polarized beam B3 having the other polarized component (S polarized component) of the laser beam B1 is reflected by the polarizing beam splitter 2, further reflected by the prism P2, and then reflected by the fixed mirror 5. Since the light passes through the λ/4 plate 2 times back and forth, the plane of polarization rotates 90 degrees and becomes a P-polarized component.
It passes through the polarized beam splitter 2 and enters the detector 6 like the other polarized beam B2.

FIG. 2 is an enlarged view of P1 and P2 in FIG. As shown in Figure 2, the difference in prism length in the traveling direction of the two divided beams is L1, and the separation distance of the two beams is L.
2, the above d1 and d2 are d1=L1-L2,
d2=L1.

Now, consider applying equation 3 to a case where there are two types of media (N=2) as in this embodiment.

In equation 4, if LH1 is the total optical path length on the movable mirror side and LH2 is the total optical path length on the fixed mirror side, then equation 4 becomes as shown below.

[0031]

[Math. 9]

[0032]

[Math. 10]

[0033] However, L0 is LH other than the prism part.
1, which is the length of the air portion common to LH2. n1
is the refractive index of air, and n2 is the refractive index of glass. Therefore, Equation 5 becomes as shown below.

[0034]

[Math. 11]

For air, changes in the refractive index due to temperature, humidity, and atmospheric pressure are corrected by changing the wavelength of the laser, and if n=n2/n1 is used, then from equation 11, L
The rate of change due to temperature is expressed by the following formula. At this time, the change in refractive index due to the change in wavelength is small, so it is ignored.

[0036]

[Math. 12]

Equation 12 can also be expressed using d1 and d2, but in this embodiment, it is easier to understand the conditions for making the temperature change rate 0 by expressing it using L1 and L2, so L1,
Indicated by L2.

At this time, assuming that the glass material is BK7, the wavelength is 632.8 nm, and the temperature is around 25°C, α
=7.1×10￣6/K, n=1.515, and the temperature change in refractive index is given by the following formula.

[0039]

[Math. 13]

Therefore, (2.8×10￣6+0.515×7.1×10￣6)
・L1=(2.8×10￣6+1.515×7.1×1
0￣6)・L2. When this is rearranged, L1=2.1×L2.

According to the above equation, it can be seen that, for example, when L2=20 mm, it is sufficient to set L1=42 mm.

FIG. 3 shows a prism of the conventional interferometer shown in FIG. Regarding this, when calculated under the same conditions, L1
= 0, so the following formula is obtained.

[0043]

[Math. 14]

[0044] Therefore, a variation of -271 nm/°C occurs.

Regarding the arrangement of the prisms when carrying out the present invention, as shown in FIG. 4, the parallelogram-shaped prism P2 is separated into two right-angled triangular prisms P5 and P7.
If this arrangement is made, the distance between the prisms P5 and P7 will vary depending on the temperature, and the thickness of the air layer will vary depending on the point around which the prism P7 expands, so this is not an appropriate arrangement. However, if the prism P1 is separated into a right triangular prism P8 and a rectangular prism P9, or into a large number of prisms, as shown in FIG. The way in which it changes is constant. However, since it is desirable that the temperature difference between the prisms be small, it is better not to separate the prism P1.

Although not an embodiment according to the present invention, FIG.
This is a diagram in which the optical path is bent by the mirror M1 instead of the beam splitter 2, and the optical path length difference does not change due to expansion of the glass due to temperature changes or changes in the refractive index, but the distance between the mirror M1 and the prisms P11 and P12 is This is undesirable because it changes with temperature.

In the above explanation, it is assumed that the influence of changes in laser wavelength due to temperature changes is small.

As described above, according to the present invention, it is possible to reduce the change in the optical path length difference caused by the change in the refractive index of the glass due to temperature change and the expansion of the glass, so that highly accurate length measurement using an interferometer is possible. It is possible.

As is clear from equation 3, the smaller the beam spacing L2 of the interferometer is, the smaller the error will be.
It is thought that the closer the two beams are brought together, the smaller the temperature difference between the two optical paths will be, so the accuracy can be further improved.

[0050]

[Effects of the Invention] Since the present invention is configured as described above, it is possible to provide an interferometer that reduces changes in the optical path length difference caused by temperature changes, and can perform position measurement with higher accuracy. can.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram showing the relationship between a laser interferometer and a stage according to the present invention.

FIG. 2 is an enlarged explanatory diagram of prisms P1 and P2 in FIG. 1;

FIG. 3 is an enlarged explanatory diagram of prisms P3 and P4 in FIG. 7;

FIG. 4 is a layout diagram of prisms placed in a position that cannot be accurately calculated.

FIG. 5 is an explanatory diagram of a second embodiment of the present invention.

FIG. 6 is a layout diagram of prisms placed in a position that cannot be accurately calculated.

FIG. 7 is an explanatory diagram showing the relationship between a laser interferometer and a stage according to the prior art.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1... Laser light source, 2... Beam splitter, 3... λ/4 plate, 4... Movable mirror, 5... Fixed mirror, 6... Detector, 7... Stage, P1 to P12... Prism, M1... Mirror.

Claims (5)

[Claims] [Claim 1] An interferometer in which a beam of light emitted from a light source is divided into a plurality of beams of light, each of which passes through one or more media and then interferes with each other, wherein one or more optical path length corrections are performed. block, and the refractive index of each medium is ni(i
= 1 to N), the physical length difference between the ray bundles for each medium is di (i = 1 to N), and the expansion and contraction of the medium excluding air is the physical length difference di for each of the above media. When αi (i=1 to N) is the rate of change per unit length and T is the temperature, d
An interferometer characterized in that the physical length li (i=1 to m) of the optical path length correction block is set so that i satisfies the following equation. 2. The optical path length correction block comprises: the optical path length correction block; a beam splitter for splitting a beam; and a reflecting mirror for bending the optical path to change the traveling direction of one of the branched beams; 2. An interferometer according to claim 1, wherein: , said beam splitter, and said optical path bending reflecting mirror are integrated into one body. 3. The interferometer according to claim 1, wherein the interferometer has a laser light source as a light source. 4. The interferometer according to claim 1, 2, or 3 includes a first reflecting mirror that serves as a reference for position measurement, and a second reflecting mirror that is attached to a measurement object and whose position is measured. have, first
An interferometer characterized in that it is a position measuring device that measures the relative distance between a second reflecting mirror and a second reflecting mirror. 5. An interference method in which a beam of light emitted from a light source is divided into a plurality of beams of light, and each of the beams of light passes through one or more media and then interferes with each other, wherein the refractive index of each medium is ni (i = 1 to N), the difference in physical length between the ray bundles for each of the above media is di (i = 1 to N), and the difference in physical length di of each of the above, excluding air, is When the rate of change per unit length due to expansion and contraction of the medium is αi (i = 1 to N) and the temperature is T, the physical length li (i = An interference method characterized in that a beam of light passes through a medium in which an angle of 1 to m) is set.